Correlation analyses of deep galaxy samples

Abstract

Methods are set out for the study of galaxy correlations using deep Schmidt plates and an automatic measuring procedure. The covariance function is defined and shown to be an objective measure of galaxy clustering. The work of previous authors on the angular covariance function and the conversion of this to the spatial covariance function is reviewed. The clustering of clusters is discussed. The form of the data used is described and the procedure for calculating the angular covariance function is set out. The form of the angular covariance function is found to be consistent with a power law of index –u.8, in agreement with previous estimates. In order to compare the amplitude of the angular covariance function for the very deep samples with that obtained from the earlier shallow samples, a cosmological generalization of Limber's formula is derived. In order to evaluate this, the distribution in distance of the galaxies in the sample is required. This is obtained via the distribution of angular diameters of the galaxies. A detailed model of the galaxy population is used to determine the expected distribution of angular diameters and the best fit to the observed counts gives the most likely parameters for the model. This in turn gives the distance distribution of the visible galaxies. It is found that the amplitude is lower than expected and it is judged that this is due to the use of very small areas which may not truly reflect the overall clustering pattern. Nonetheless, it is felt that the methods described will prove a valuable and powerful means of exploring the large scale distribution of galaxies.